where \(\delta _{I_{3}^{\prime }, I_{3}}\)  is the Kronecker delta, \(\psi _{\varepsilon , \mathbf {p}, I_{3}}\)  is wave function () of the “in"
state with momentum \(\mathbf {p}=(p,0)\)  and isospin \(I_{3}\) , \(u_{\varepsilon ,\mathbf {p}^{\prime }, I_{3}^{\prime }}\)  is the spinor-isospinor amplitude of wave
function () of the “out" state with momentum \(\mathbf {p}^{\prime }= (p\cos (\theta ), p\sin (\theta ))\)  and isospin \(I_{3}^{\prime }\) , \(f_{I_{3}^{\prime }, I_{3}}\left(p, \theta \right)\)  is the scattering amplitude, and the
factor \(-i\)  under the square root sign is introduced for convenience.
Using Eqs. (), (REF ), (REF ), and standard methods from
the theory of scattering [1]}, [2]}, we obtain an expansion of
the scattering amplitude \(f_{I_{3}^{\prime },I_{3}}\left( p, \theta \right)\)  in
terms of the partial scattering amplitudes \(f_{I_{3}^{\prime },I_{3}}^{\left(m\right)}\left( p \right)\)
\(f_{I_{3}^{\prime },I_{3}}\left(p, \theta \right) =e^{-iI_{3}^{\prime }\left(n+1\right) \theta }\sum \limits _{m}f_{I_{3}^{\prime },I_{3}}^{\left( m\right)}\left( p\right) e^{i m \theta }. \) 
